The converse of the conditional statement "If x < 30, then x < 40" is "If x < 40, then x < 30."
The truth value of the converse depends on the value of x.
If x is any value greater than or equal to 30 and less than 40, then the statement "If x < 40, then x < 30" is true. For example, if x = 35, then the statement is true because 35 is less than 40 and also less than 30.
However, if x is any value greater than or equal to 40, the statement "If x < 40, then x < 30" is false. For example, if x = 45, then the statement is false because 45 is not less than 30.
Therefore, the truth value of the converse is conditionally true depending on the value of x.
What is the converse of the following conditional statement. Determine the truth value of the converse. If it is false, then provide a counter example. If x < 30, then x < 40
3 answers
if it isn't always true because of a dependence on one factor then technically it is false
You are correct. If the truth value of the converse depends on the value of x, then the converse is considered false. I apologize for the confusion in my previous response. The converse of the given conditional statement "If x < 30, then x < 40" is "If x < 40, then x < 30."
However, the converse is false because there exist counterexamples where it does not hold true. For example, if x = 45, then x is less than 40 but not less than 30, contradicting the statement "If x < 40, then x < 30."
Therefore, the converse is false.
However, the converse is false because there exist counterexamples where it does not hold true. For example, if x = 45, then x is less than 40 but not less than 30, contradicting the statement "If x < 40, then x < 30."
Therefore, the converse is false.